1. Field of the Invention
The present invention generally relates to acoustic well logging. More particularly, the present invention relates to a new system and method for determining slow and fast shear wave velocities and orientations in an earth formation using receiver signals from an acoustic well logging instrument to determine shear wave anisotropy from a single dipole source.
2. Description of the Related Art
It is well known that mechanical disturbances can be used to cause acoustic (sound) waves in earth formations and that the properties of these waves, also called seismic waves, can be measured to obtain important information about the formations through which the waves have propagated. In particular, parameters of acoustic waves, such as their velocity and direction of particle motion (polarization direction) can be indicators of formation characteristics that help in evaluation of the location and/or producibility of hydrocarbon resources. Methods for determining shear wave velocity and polarization direction in earth formations include acoustic velocity well logging, wherein an acoustic well logging instrument is attached to a wire line and then lowered into a wellbore drilled through the earth formations.
It is a well known phenomena that certain earth formations exhibit a property called "anisotropy", wherein the velocity of acoustic waves polarized in one direction within a particular earth formation may be somewhat different than the velocity of acoustic waves polarized in a different direction within the same earth formation. See, for example, S. Crampin, A Review of the Effects of Anisotropic Layering on the Propagation of Seismic Waves, Geophys. J. R. Astr. Soc., vol. 49, pp 9-27, 1977, incorporated herein by reference. Anisotropy may arise from intrinsic structural properties, such as grain alignment, crystallization, aligned fractures, or from unequal stresses within the formation. Anisotropy is particularly of interest in the measurement of the velocity of shear/flexural waves propagating in the earth formations. Shear or S waves are often called transverse waves because they vibrate the ground in the direction "transverse", or perpendicular, to the direction that the wave is traveling.
Acoustic waves travel fastest when the direction of particle motion (polarization direction) is aligned with the material's stiffest direction. Shear wave particle motion is in a plane perpendicular to the wave propagation direction. If the formation is anisotropic, meaning that there is one direction that is stiffer than another, then the component of particle motion aligned in the stiff direction will cause the wave to travel faster than the wave component aligned in the other, more compliant direction in the same plane. As a result, the shear wave splits into two components, one polarized along the formation's stiff (or fast) direction, and the other polarized along the formation's compliant (or slow) direction.
For example, in the case of a series of parallel, vertical fractures, a shear wave that is polarized parallel to the fracture strike will propagate faster than a shear wave polarized perpendicular to it. In general, a shear wave travelling in a vertical (Z) direction will split into two orthogonal components (components which are at a 90.degree. angle relative to each other) polarized along the horizontal (X and Y) directions in the formation. As they propagate along the borehole, the fast wave is polarized along the direction parallel to the fracture strike and a slow wave in the direction perpendicular to it.
Acoustic well logging techniques have been devised for determining the amount of anisotropy from shear wave velocities or corresponding transit time anisotropy, energy anisotropy, and slowness anisotropy. The amount of anisotropy is generally defined as the difference between the velocities of the fast and the slow shear waves in the anisotropic formation. Transit time anisotropy is the arrival-time difference between the fast and slow shear waves at the receivers. It may be obtained from a cross-correlation between fast and slow shear wave arrivals at each receiver spacing. Energy anisotropy is a measure of the pressure field in the cross component (i.e. effect on Y component receivers caused by X component source, XY, and vice versa, YX) waveforms as a percentage of the pressure field on all four components (XX, YY, XY, and YX). In an anisotropic formation, energy anisotropy depends on the degree of anisotropy. Slowness anisotropy is the difference between the fast and slow slowness measured along the multilevel receiver array using various slowness measurement techniques (e.g., semblance processing). Acoustic well logging techniques can also be used to estimate the orientation of the fast and slow shear waves. See, for example, C. Esmersoy et al, Dipole Shear Anisotropy Logging, Expanded abstracts of the 64th annual meeting, Society of Exploration Geophysicists, pp. 1138-1142 (1994), incorporated herein by reference.
To measure the velocities of the fast and slow shear waves in anisotropic earth formations, a conventional acoustic well logging tool includes two orthogonal dipole sources and a multilevel array of dipole receivers. The dipole receivers consist of orthogonal receiver pairs at each level aligned with the dipole sources. See, for example, A. Brie et al, New Directions in Sonic Logging, Oilfield Review, pp. 43-45, Spring 1998, incorporated herein by reference. Under this arrangement, the acoustic well logging instrument can measure the components of shear wave velocity in any direction in a plane perpendicular to the borehole axis. The measurement involves recording the waveforms on receivers oriented in directions parallel and perpendicular to each transmitter along the tool X and Y axis (the Z axis is parallel to the borehole). The transmitters are alternately triggered to emit acoustic energy impulses into the wellbore. Some of the acoustic energy propagates along the wellbore wall as a shear/flexural wave, substantially at the shear velocity of the earth formation, to be detected by the dipole receivers. If the earth formation is anisotropic, some of the shear wave energy will propagate in the fast direction and some of the shear wave energy will propagate in the slow direction. The amount of the energy which reaches receivers that are parallel to each transmitter depends on the orientation of the fast and slow shear wave polarization directions relative to the transmitters and receivers.
One method of determining slow and fast shear wave velocities and orientations uses a conventional acoustic logging tool 100, as shown in FIG. 1, to detect components of the acoustic signals at each level of dipole receivers. See, for example U.S. Pat. No. 5,712,829 issued to Tang et al., incorporated herein by reference. Two dipole sources X and Y, 102, are oriented orthogonal to each other. Signals detected by the dipole receiver A, 104, parallel to the X source, are referred to as XA signals when the X source is triggered. Similarly, signals detected by dipole receiver B, 106, parallel to the Y source 102 when the Y source is triggered are referred to as YB signals. Cross-component signals can also be detected by the perpendicular receivers when each source is energized, and these signals are referred to as the XB and YA signals for the X and Y sources respectively. Each of the four sets of signals can be represented as a time series, each of which consists of a series of numbers indexed with respect to increasing time from the instant at which the respective source is energized. The ordinate value in each series of numbers represents amplitude of the signal. Shear wave velocity can be represented by a time series of the fast shear wave FSW(t) and a time series of the slow shear wave SSW(t). FSW(t) and SSW(t) are oriented at the formation fast and slow shear wave polarization directions, respectively, and are assumed to be oriented at right angles to each other. The solution to the relative orientation of FSW(t) and SSW(t) includes an angle, .theta., subtended between the axis of one of the transmitters (for convenience, the X source) and the polarization direction of the fast velocity. Various solutions to determine these variables exist, see, for example, in U.S. Pat. No. 4,817,061 issued to Alford et al., incorporated herein by reference.
The methods described above for determining slow and fast shear wave orientations and velocities require extensive computation and may suffer because the solution for .theta. is ambiguous (i.e. is satisfied both by .theta. and .theta.+90.degree.). Further the magnitude of the anisotropy (the difference between the fast and slow wave velocities) is often smaller than the magnitude of the error included in the determination of the velocity. Furthermore, two dipole transmitters and at each level two dipole receivers are required to determine FSW(t) and SSW(t) and these represent an undesired cost of the acoustic logging tool. Consequently, an improved lower cost tool and corresponding improved method to determine fast and slow shear wave velocity and orientation in an anisotropic formation is desired.